A theory of the staircase voltammetry in a thin-layer cell is developed. The influence of the cell thickness and the redox reaction rate constant on the current and the peak potentials is analyzed. For moderately thick cells, the kinetic maximum is predicted. The relationship between peak currents and the square root of the scan rate is not linear and the response may entirely vanish if the redox reaction is fast, the cell is very thin and the scan rate is slow.
Model:A staircase voltammetry of a simple redox reaction A + n e = B(1) in a thin-layer cell is considered. It is assumed that both species A and B are solution soluble and that the cell consists of a planar electrode which is situated at the distance L from the parallel electroinactive wall. A distribution of the reactant and the product of this redox reaction in the space between two parallel infinite planes is defined by the differential equations [7, 151:with initial and boundary conditionswhere cA, c, and c i are concentrations, t and x are the time and the space variables, L is the distance between the parallel planes, D is the diffusion coefficient, S is the electrode surface area, i is the current, E is the electrode potential, E o is the standard potential, k, is the standard reaction rate constant, a! is the transfer coefficient and n, F , R and T have their usual meanings.The solutions of Equations 2 and 3 can be obtained using Laplace transformations and the numerical integration method of Nicholson and Olmstead [24]. The dimensionless current q5 = i (nFSck)-1(dD)"2 can be calculated by the system of recursive formulae:' is the dimensionless cell thickness, h = k,(~/D)"' is the dimensionless rate constant, 7 = AE/v is the step duration in staircase voltammetry, AE is the potential increment, z, is the scan rate and d = 7/25 is the time increment for the numerical integration.If the redox reaction ( Fig. 1) is fast and reversible, the response in the cyclic staircase voltammetry depends on the dimensionless cell thickness w = 5 L(D7)-"'. The relationship between dimensionless peak current q5p and the logarithm of the parameter w is shown in Figure 1. Under the conditions of semiinfinite diffusion (log w >